Method for identifying fertility transformation characteristics of photo-thermo-sensitive two-line sterile line of rice at high altitude

Abstract

The invention discloses a method for identifying fertility transformation characteristics of a rice photo-thermo-sensitive two-line sterile line at a high altitude. The method comprises the following steps: (1) selecting a high-altitude field for planting rice; (2) sowing the sterile line by stages and transplanting seedlings; (3) measuring the field temperature of the planting plot; (4) carrying out regular bagging selfing and pollen microscopic examination on the rice after heading; and (5) processing data obtained by bagging selfing and pollen microscopic examination by adopting a logistic regression model. According to the method, a logistic regression model is constructed, the sterile line is placed in a fertility transformation critical state by utilizing a high-altitude planting environment, the fertility character of the sterile line is investigated and is associated with the daily average temperature and the daily minimum temperature of a sterile line fertility sensitive period, and the relationship between the environment temperature and the fertility transformation of the sterile line is determined; identifying the fertility transformation characteristic of the sterile line, and calculating the fertility transformation starting point temperature.

Description

Technical Field

[0001] The invention relates to the field of rice breeding, and in particular to a method for identifying fertility conversion characteristics of a photothermosensitive two-line sterile rice line at high altitude. Background Art

[0002] Two-line hybrid rice has gotten rid of the constraints of restoration and protection during the three-line hybrid rice mating process, showing the strong superiority of free mating. After 30 years of development, it has become the mainstream of hybrid rice. The sterile line shows male sterility under long-day high temperature for the production of hybrid rice seeds, and shows partial recovery of male fertility under short-day low temperature for the reproduction of the sterile line itself. Its fertility performance is closely related to the light and temperature conditions of the growth environment. The temperature point at which the sterile line undergoes the transformation from male sterility to partial fertility is called the starting temperature of fertility transformation of the sterile line (hereinafter referred to as the starting temperature). The relatively low starting temperature provides a guarantee for the production and application of the sterile line, and is also an important basis for the approval of two-line hybrid rice varieties.

[0003] At present, the starting temperature for identifying sterile lines is adopted in artificial climate chamber or cold water pool. The treatment temperature is set to an average temperature of 23.5℃ for 6 days, and the stem ears that are in the 5th and 6th stages of ear differentiation during low temperature treatment are inspected. The inspection indicators are the self-pollination fruit setting rate of bagging and the percentage of sterile pollen. It is believed that under this treatment condition, the starting temperature of the sterile line with bagging fruit setting less than 2% and sterile pollen more than 99% is lower than 23.5℃, which is safe in production and meets the requirements of variety approval.

[0004] In the artificial climate chamber treatment, due to the small specific heat of air, the temperature fluctuates greatly and is seriously uneven in space. The light quality and intensity in the chamber are very different from natural light, and the treatment results are inaccurate. The space in the artificial climate chamber is limited, and the number of samples finally included in the statistics is small, so the identification results are not convincing. Before and after the treatment in the climate chamber, the treated plants are exposed to higher temperatures in midsummer, which will affect the treatment results. In addition, the potting work of rice requires a lot of manpower and material resources.

[0005] The cold water pool treatment requires flooding to the growth point of the young panicle of the sterile line, with some leaves exposed above the water surface. Long-term low-temperature flooding will cause stress to the treated individual plants of the sterile line, and some leaf tillers will turn yellow or wither, or even show very serious stress. This stress is bound to cause deviations in the identification results, and there may be large deviations. Due to the high specific heat and flow viscosity of water, the controllable temperature change in the pool on a single day cannot be achieved, which is inconsistent with the temperature change on the same day of the simulated low temperature situation in midsummer, and cannot reflect the effect of the daily minimum temperature in the fertility transformation process. The rice plants are exposed to the high temperature environment in midsummer before and after the cold water treatment, which will definitely affect the results of the cold water treatment. Due to the differences in the development of different tillers of the same rice plant, the number of rice tillers that actually produce the treatment effect is small, and the number of observation samples finally included in the statistics is very small, and the results are not convincing. The cold water pool model requires the construction of a cold water pool and complicated potting operations. The construction and operation process consumes a lot of financial, material and energy resources, and the whole process is ineffective.

[0006] In the work of variety approval, in the absence of better alternatives, artificial climate chambers and cold water pools are still the only two methods to identify the starting temperature of sterile lines. Whether the starting temperature of sterile lines is lower or higher than 23.5℃ is used to determine whether the two-line sterile lines of rice are safe for use. Due to the many drawbacks of the two methods, their results are not reliable enough. In variety approval, new and more effective methods are urgently needed to identify the starting temperature of sterile lines.

[0007] The attempt to study sterile lines using the low temperature of midsummer at high altitudes has a long history, but the previous work has not been very effective and has not been very successful. The reasons are: there was no suitable automatic temperature recorder at that time, so the temperature recording work could not be completed, and the fertility performance of the sterile lines could not be linked to the actual temperature; at that time, transportation in high-altitude mountainous areas was inconvenient, farmland facilities were backward, life and work were very difficult, and experimental work could not be carried out continuously; if there was a cold soaked shade field, the sterile lines could not grow normally, and the experiment could not be carried out normally. Later, artificial climate chambers and cold water pools were available, and few people used high altitudes to study sterile lines.

[0008] However, high altitude conditions have obvious advantages: in suitable high altitude fields during the rice growing season, the environmental temperature is similar to the starting temperature of the sterile line, and the sterile lines are mostly in the state of fertility transformation, which is an ideal place to study the relationship between the fertility transformation of the sterile line and temperature. In addition, the naturally formed daily minimum temperature can be fully reflected; high altitude fields are in an open natural space, with natural light, no flooding stress, unlimited working capacity, and low temperatures that will not cause low temperature stress. The temperature is evenly distributed within the planting field, the daily minimum temperature is naturally displayed, there is no potted work, and the operation is simple.

[0009] Nowadays, the transportation and living conditions in high-altitude mountainous areas have been significantly improved. The use of automatic temperature recorders can continuously record the actual field temperature, providing a guarantee for the implementation of high-altitude field plots to study the fertility conversion of sterile lines. However, the field temperature of rice growth cannot be controlled artificially, and it is necessary to establish a suitable mathematical model to fully link the field temperature with the fertility conversion of sterile lines. This mathematical model is very different from the data processing method of artificial climate chambers or cold water pools. Summary of the invention

[0010] The purpose of the present invention is to provide a method for identifying the fertility transformation characteristics of sterile lines by low temperature in midsummer at high altitudes, and to utilize the natural low temperature at high altitudes to identify the fertility transformation characteristics of sterile lines. The operation is simple, and the amount of data is expanded to make the analysis results more accurate and reliable. There is no need for artificial climate boxes or cold water pools to utilize facilities to simulate low temperatures, thus saving a lot of manpower, material resources and financial resources.

[0011] In one aspect of the present invention, the present invention provides a method for identifying the fertility conversion characteristics of a photothermosensitive two-line sterile rice line at high altitude. According to an embodiment of the present invention, the method comprises the following steps:

[0012] (1) Select high-altitude fields to grow rice;

[0013] (2) Sterile lines are sown in stages and seedlings are transplanted;

[0014] (3) Determine the field temperature of the planting plot;

[0015] (4) After heading, the rice is regularly bagged and selfed and the pollen is examined under a microscopic microscope;

[0016] (5) The data obtained from bagging self-pollination and pollen microscopy were processed using a logistic regression model.

[0017] In addition, the method for identifying fertility transformation of rice photothermosensitive two-line sterile lines in fields at different altitudes according to the above embodiment of the present invention may also have the following additional technical features:

[0018] In some embodiments of the present invention, in step (1), conventional methods are adopted for seed soaking, germination and seedling raising. After the seedlings are 25-30 days old, the sterile seedlings are transplanted to the high-altitude fields and managed in the field by conventional methods.

[0019] In some embodiments of the present invention, in step (1), the high-altitude field is located in the middle and lower reaches of the Yangtze River at 29.5-30.5° north latitude, with an altitude of 700-750 meters, and multiple automatic temperature recorders are installed in the sterile line transplanting field and are set to measure the temperature at the same time.

[0020] In some embodiments of the present invention, in step (4), the sterile lines are bagged when they begin to head, and ears with stems that are 2 cm long and have not yet flowered are selected for bagging and self-pollination, and the percentage of fruiting spikelets to total spikelets is used as the bagging fruit setting rate.

[0021] In some embodiments of the present invention, in step (4), samples are taken regularly from the beginning of heading to the completion of heading of the identified sterile line, and the stem ears that have not bloomed are selected for microscopic examination. The anthers of 5-6 spikelets are randomly taken from each sampled ear to make a pollen microscopic observation slide, and the pollen is stained with 2% KI-I2 solution, pressed into a slide, and observed under an optical microscope.

[0022] In some embodiments of the present invention, in step (5), the mathematical model of bagging self-crossing is as follows:

[0023] p 实i =exp(β 实0 +β 实平 *t 平i +β 实低 *t 低i ) / (1+exp(β 实0 +β 实平 *t 平i +β 实低 *t 低i ))

[0024] p 不i =1 / (1+exp(β 实0 +β 实平 *t 平i +β 实低 *t 低i ))

[0025] p 实i +p 不i =1,m 实i +m 不i =1;

[0026] In the formula, p 实i and p 不i They represent the theoretical probability of the i-th self-crossing bag to produce fruit or not, β 实0 , β 实平 and β 实低 are the parameters of the model, representing the intercept of the fruiting rate in the logistic regression model, the slope of the daily average temperature, and the slope of the daily minimum temperature, t 平i and t 低i are the average daily temperature and the average daily minimum temperature of the sampling plot on the 13th to 15th day from the bagging date of the i-th self-pollination bag, m 实i and m 不iThey represent the actual fruit setting rate and non-fruit setting rate of rice ears in the i-th self-pollination bag respectively;

[0027] The self-fertilization rate of 2% is taken as the critical point of fertility transformation of the sterile line. According to the definition of the starting point temperature of the sterile line, the starting point temperature T = t 平 =t 低 , where t 平 and t 低 They represent the daily average temperature and daily minimum temperature of the sterile line during its sensitive period. The calculation formula for the fertility threshold temperature of the sterile line is: T = (-3.892-β 实0 ) / (β 实平 +β 实低 ).

[0028] In some embodiments of the present invention, in step (5), the calculation method of bagging firmness is as follows:

[0029] Use the maximum likelihood method to solve:

[0030]

[0031] Take the natural logarithm of the likelihood:

[0032]

[0033] The maximum likelihood theory holds that the likelihood value L 实 The parameter value in the largest case is an unbiased estimate of the model, which is also l 实 It is also the largest;

[0034] Ask for l 实 Maximum, l 实 β 实0 , β 实平 and β 实低 The partial derivative of DP is 0; 实0 , DP 实平 and DP 实低 Respectively expressed as l 实 β 实0 , β 实平 and β 实低 Partial guide;

[0035]

[0036] Let parameter vector B = (β0, β 实平 ,β 实低 ) T and deflection vector F = (PD 实0 ,PD 实平 ,PD 实低 ) T, F is the function vector of B, and the Jacobi matrix f used for Newton iteration is the partial derivative matrix function of F with respect to B;

[0037] The initial value is set artificially, and the iterative formula is: B (m+1) =B (m) -f (-1) (B (m) )*F(B (m) ), m is the number of iterations, iterate to ||B (m+1) -B (m) ||<10 -5 In case B (m+1) The value is the B parameter vector value, B (m) and B (m+1) Respectively represent the B vector values ​​after the mth and m+1th iterations, f (-1) (B (m) ) represents the inverse matrix of the m-th iteration of the f matrix, F(B (m) ) represents the F vector of iteration m.

[0038] In some embodiments of the present invention, in step (5), the mathematical model of pollen microscopy is as follows:

[0039] p 典i =exp(β 典0 +β 典平 *t 平i +β 典低 *t 低i ) / (1+exp(β 典0 +β 典平 *t 平i +β 典低 *t 低i )+exp(β 园0 +β 园平 *t 平i +β 园低 *t 低i )+exp(β 染0 +β 染平 *t 平i +β 染低 *t 低i ))

[0040] p 园i =exp(β 园0 +β 园平 *t 平i +β 园低 *t 低i ) / (1+exp(β 典0 +β 典平 *t 平i +β 典低 *t 低i) + exp(β 园0 + β 园平 * t 平i + β 园低 * t 低i ) + exp(β 染0 + β 染平 * t 平i + β 染低 * t 低i ))

[0041] p 染i = exp(β 染0 + β 染平 * t 平i + β 染低 * t 低i ) / (1 + exp(β 典0 + β 典平 * t 平i + β 典低 * t 低i ) + exp(β 园0 + β 园平 * t 平i + β 园低 * t 低i ) + exp(β 染0 + β 染平 * t 平i + β 染低 * t 低i ))

[0042] p 可i = 1 / (1 + exp(β 典0 + β 典平 * t 平i + β 典低 * t 低i ) + exp(β 园0 + β 园平 * t 平i + β 园低 * t 低i ) + exp(β 染0 + β 染平 * t 平i + β 染低 * t 低i ))

[0043] p 典i + p 园i + p 染i + p 可i = 1m 典i + m 园i + m 染i + m 可i = 1

[0044] In the formula, p 典i、p 园i 、p 染i 、p 可i represent the theoretical probabilities of typical failed pollen, round failed pollen, stained failed pollen and stainable pollen in the i-th microscopic examination respectively; as the parameter value of the model, β 典0 , β 典平 and β 典低 are the intercept of pollen failure, the slope of daily average temperature and the slope of daily minimum temperature, respectively. 园0 , β 园平 and β 园低 are the intercept of pollen abortion, the slope of daily average temperature and the slope of daily minimum temperature, β 染0 , β 染平 and β 染低 are the intercept of pollen atrophy, the slope to the daily average temperature, and the slope to the daily minimum temperature, respectively; t 平i and t 低i The average of the daily average temperature and the daily minimum temperature of the sampling plot on the 13th to 15th day before the i-th bagging date, m 典i 、m 园i 、m 染i and m 可i They represent the ratios of typical failed, round failed, stained failed and stainable pollen in the i-th microscopic observation respectively.

[0045] In some embodiments of the present invention, in step (5), the calculation method of pollen microscopy is as follows:

[0046] A similar maximum likelihood method is used to solve:

[0047]

[0048] The likelihood value L 花 Take the natural logarithm:

[0049]

[0050] According to the maximum likelihood theory, the likelihood value L 实 The parameter value under the maximum condition is the unbiased estimate of the model. 实 Maximum; let B 花 =(β 典0 ,β 典低 ,β 园0 ,β 园平 ,β 园低 ,β 染0 ,β 染平 ,β 染低 ) T As the parameter vector of the model, according to the theory of calculus, l 实 To B 花 The deflection vector F花 When l is 0, 实 maximum.

[0051] F 花 =(PD 典0 ,PD 典平 ,PD 典低 ,PD 园0 ,PD 园平 ,PD 园低 ,PD 染0 ,PD 染平 ,PD 染低 ) T ;

[0052] Let vector F 花 That is, 9 partial derivatives are 0, 9 equations are constructed, and 9 parameter values ​​are solved. The 9 equations are nonlinear, and highly approximate solutions are obtained through Newton iteration. The Jacobi matrix f used in Newton iteration is 花 Yes F 花 To B 花 The partial derivative matrix function of ;

[0053] The initial value is set artificially, and the iteration formula is: m refers to the number of iterations. The situation Value is B 花 parameter vector value; and Respectively represent B after the mth and m+1th iterations 花 vector value, Indicates the mth iteration of f 花 The inverse matrix of the moment, represents the F of the mth iteration 花 vector.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] 1. The present invention utilizes the natural low temperature at high altitude, not the processing temperature set by the facility, which is highly similar to the fertility fluctuation caused by the low temperature in midsummer encountered by the sterile line. The identification result is highly consistent with the actual situation and has high production utilization value;

[0056] 2. The present invention can be used for bagging and sampling under a microscope in a field environment without the need for special facilities and equipment, thereby eliminating the need for artificial climate boxes or cold water pools for identification work and potted plant labor, thus saving manpower and material resources;

[0057] 3. The present invention has a huge test capacity and can obtain a large amount of data through large-scale self-pollination bagging and pollen microscopy. A logistic regression model is constructed and the maximum likelihood method is used to process the data with high credibility. It is the first attempt to calculate the starting temperature of the sterile line and the statistical analysis of the pollen microscopy data. DETAILED DESCRIPTION

[0058] The following will be described clearly and completely in conjunction with the technical solutions implemented in the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] The method for identifying the fertility transformation characteristics of a photothermosensitive two-line sterile rice line at high altitude comprises the following steps:

[0060] 1. Selection of planting plots

[0061] In the one-season indica rice planting area in the middle and lower reaches of the Yangtze River, within the area of ​​29.5-30.5° north latitude, high-altitude fields were selected, with an altitude of 700-750 meters. The fields were required to have convenient transportation, convenient irrigation and drainage, less shade, and no cold soaking.

[0062] 2. Staged sowing and seedling transplanting

[0063] From late April to mid-June, sterile seeds were sown every 10 days in low altitude areas (below 100 meters above sea level), for a total of 6 stages, and conventional methods were used for seed soaking, germination and seedling raising.

[0064] When the seedlings are 25-30 days old, the sterile seedlings are transplanted to the high-altitude planting site. Each sterile line is transplanted into 120-150 holes, with one seed seedling per hole. The transplanting density is 20×20cm, and the field management is carried out using conventional methods.

[0065] 3. Determination of field temperature

[0066] 6-8 automatic temperature recorders were installed in high-altitude fields to record field temperature from June 20 to August 30. All automatic temperature recorders were set to measure temperature at the same time, measuring and recording once every 6 minutes, 240 times a day, without interruption.

[0067] 4. The bagging is firm

[0068] Bagging starts on July 1 or when the sterile line starts to head (after July 1), and the bags are put on every 3 days until August 15 or when the sterile line starts to head (before August 15).

[0069] Select the ears with stems that have not bloomed for 2 cm and use them for bagging and self-pollination, and mark the date of bagging on the self-pollination bag.

[0070] Each time, 15-20 stem spikes were taken for bagging, and the percentage of fruiting spikelets to total spikelets was taken as the bagging fruit setting rate. It was required that no less than 150 self-pollinated bags be included in the final statistical analysis.

[0071] 5. Pollen microscopy

[0072] Sampling began on July 1 or when the sterile lines were identified to have started heading (after July 1), and sampling was conducted every 3 days until August 15 or when the sterile lines were identified to have completed heading (before August 15).

[0073] Select stem spikes about 2 cm in size that have not yet bloomed, and take 20-30 of them each time for pollen microscopy.

[0074] Anthers of 5-6 spikelets were randomly selected from each sampled spike to make a pollen microscopic observation slide, which was then stained and pressed with 2% KI-I2 solution and observed under an optical microscope at 100 times magnification. The pollen of the sterile line was divided into four categories: typical pollen, with irregular and small pollen grains, and no staining; round pollen, with round pollen grains, basically normal size, and no staining; stained pollen, with round pollen grains, normal size, uneven staining, less than 2 / 3 of the black staining part or light staining; normal pollen, with round pollen grains, normal size, and black staining.

[0075] Three representative fields of view are selected from each slide for observation and counting. The percentage of different types of pollen is generally calculated based on the percentage of the actual number of each pollen type in the total pollen amount. The number of microscopic slides included in the final statistical analysis is required to be no less than 250.

[0076] 6. Data processing

[0077] 6.1 Model construction

[0078] 6.1.1 Bagging Self-pollination

[0079] p 实i =exp(β 实0 +β 实平 *t 平i +β 实低 *t 低i ) / (1+exp(β 实0 +β 实平 *t 平i +β 实低 *t 低i ))

[0080] p 不i =1 / (1+exp(β 实0 +β 实平 *t平i +β 实低 *t 低i ))

[0081] p 实i +p 不i =1 m 实i +m 不i =1.

[0082] Among them, p 实i and p 不i are the theoretical probabilities (expressed as decimals) of the i-th self-pollination bag being fruitful or not, β 实0 , β 实平 and β 实低 are the parameters of the model, representing the intercept of the model, the slope of the daily mean temperature and the slope of the daily minimum temperature, t 平i and t 低i The average daily temperature and the average daily minimum temperature of the sampling plot on the 13th to 15th day before the i-th best bagging date, m 实i and m 不i They respectively represent the actual fruit set rate and non-fruit set rate (expressed as decimals) of the i-th bag.

[0083] The self-fertilization rate of 2% is taken as the critical point of fertility transformation of the sterile line, and the starting point temperature T is defined according to the starting point temperature of the sterile line. 平 =t 低 The calculation formula of the fertility threshold temperature of the sterile line is: T = (-3.892-β 实0 ) / (β 实平 +β 实低 ), the lower the starting temperature of the sterile line, the better the fertility conversion characteristics.

[0084] 6.1.2 Pollen microscopy

[0085] p 典i =exp(β 典0 +β 典平 *t 平i +β 典低 *t 低i ) / (1+exp(β 典0 +β 典平 *t 平i +β 典低 *t 低i )+exp(β 园0 +β 园平 *t 平i +β 园低 *t 低i )+exp(β 染0 +β 染平 *t 平i +β染低 *t 低i ))

[0086] p 园i =exp(β 园0 +b 园平 *t 平i +b 园低 *t 低i ) / (1+exp(β 典0 +b 典平 *t 平t +b 典低 *t 低i )+exp(β 园0 +b 园平 *t 平i +b 园低 *t 低i )+exp(β 染0 +b 染平 *t 平i +b 染低 *t 低i ))

[0087] p 染i =exp(β 染0 +b 染平 *t 平i +b 染低 *t 低i ) / (1+exp(β 典0 +b 典平 *t 平i +b 典低 *t 低i )+exp(β 园0 +b 园平 *t 平i +b 园低 *t 低i )+exp(β 染0 +b 染平 *t 平i +b 染低 *t 低i ))

[0088] p 可i =1 / (1+exp(β 典0 +b 典平 *t 平i +b 典低 *t 低i )+exp(β 园0 +b 园平 *t 平i +b 园低 *t 低i )+exp(β 染0 +b 染平 *t平i +β 染低 *t 低i ))

[0089] p 典i +p 园i +p 染i +p 可i =1

[0090] m 典i +m 园i +m 染i +m 可i =1

[0091] p 典i 、p 园i 、p 染i 、p 可i are the theoretical probabilities (expressed as decimals) of typical failed pollen, round failed pollen, stained failed pollen and stainable pollen in the i-th microscopic examination; β is the parameter value of the model, 典0 , β 典平 and β 典低 are the intercept of pollen failure, the slope of daily average temperature and the slope of daily minimum temperature, respectively. 园0 , β 园平 and β 园低 are the intercept of pollen abortion, the slope of daily average temperature and the slope of daily minimum temperature, β 染0 , β 染平 and β 染低 are the intercept of pollen atrophy, the slope to the daily average temperature, and the slope to the daily minimum temperature, respectively; t 平i and t 低i The average of the daily average temperature and the daily minimum temperature of the sampling plot on the 13th to 15th day before the i-th bagging date, m 典i 、m 园i 、m 染i and m 可i They represent the ratios of typical failed, round failed, stained failed and stainable pollen in the i-th microscopic observation (expressed as decimals).

[0092] The AIC value was used to eliminate parameters with low effects and retain parameters with high effects. The final result reflected the pollen response form of the sterile line during the fertility conversion period.

[0093] 6.2 Calculation method

[0094] 6.2.1 Bagging is strong

[0095] Use the maximum likelihood method to solve:

[0096]

[0097] Take the natural logarithm of the likelihood:

[0098]

[0099] The maximum likelihood theory holds that the likelihood value L 实 The parameter value in the largest case is an unbiased estimate of the model, which is also l 实 is also the largest. From the theory of calculus, we know that if we want to find l 实 Maximum, must be 实 β 实0 , β 实平 and β 实低 The partial derivative of DP is 0; 实0 , DP 实平 and DP 实低 Respectively expressed as l 实 β 实0 , β 实平 and β 实低 Partial derivative.

[0100]

[0101] Set the three partial derivatives to 0, construct three equations, and solve the three parameter values. Since the three equations are nonlinear, it is impossible to get an accurate analytical solution, and only a highly approximate solution can be obtained through the Newton iteration method.

[0102] Let parameter vector B = (β0, β 实平 ,β 实低 ) T and deflection vector F = (PD 实0 ,PD 实平 ,PD 实低 ) T , F is the function vector of B. The Jacobi matrix f used in Newton iteration is the partial derivative matrix function of F with respect to B. The derivation results are as follows.

[0103]

[0104] Artificially set the initial value B (0) =(-1,-0.04,-0.05) T , the iteration formula is: B (m+1) =B (m) -f (-1) (B (m) )*F(B (m) ), m refers to the number of iterations, iterating to ||B (m+1) -B (m) ||<10 -5 In case B (m+1) The value is the B parameter vector value. (m) and B (m+1)Respectively represent the B vector values ​​after the mth and m+1th iterations, f (-1) (B (m) ) represents the inverse matrix of the m-th iteration of the f matrix, F(B (m) ) represents the F vector of iteration m.

[0105] It is required that no less than 150 selfing bags be included in the final statistical analysis, and the calculation program should be written in R language.

[0106] 6.2.2 Pollen microscopy

[0107] A similar maximum likelihood method is used to solve the problem.

[0108]

[0109] Take the natural logarithm of the likelihood:

[0110]

[0111] According to the maximum likelihood theory, the likelihood value L 实 The parameter value under the maximum condition is the unbiased estimate of the model. 实 Maximum. Let B = (β 典0 ,β 典低 ,β 园0 ,β 园平 ,β 园低 ,β 染0 ,β 染平 ,β 染低 ) T As the parameter vector of the model, according to the theory of calculus, l 实 To B 花 The deflection vector F 花 When l is 0, 实 maximum.

[0112] F 花 =(PD 典0 ,PD 典平 ,PD 典低 ,PD 园0 ,PD 园平 ,PD 园低 ,PD 染0 ,PD 染平 ,PD 染低 ) T .

[0113]

[0114] Let vector F 花That is, 9 partial derivatives are 0, 9 equations are constructed, and 9 parameter values ​​are solved. Since the 9 equations are nonlinear, it is impossible to obtain an accurate analytical solution, and only a highly approximate solution can be obtained through the Newton iteration method.

[0115] Jacobi matrix f for Newton iteration 花 Yes F 花 To B 花 The partial derivative matrix function of , the derivation results are as follows.

[0116]

[0117]

[0118] Manually set the initial value:

[0119]

[0120] The formula for iteration is: m refers to the number of iterations. The situation Value is B 花 Parameter vector value. Among them, and Represents B after the mth and m+1th iterations respectively 花 vector value, Indicates the mth iteration of f 花 The inverse matrix of the moment, represents the F of the mth iteration 花 vector.

[0121] The model has a total of 9 parameters and may be overfitted. The AIC value is used to eliminate redundant parameters to refine the model. The calculation formula is AIC=2k-2ln(L), where k is the number of parameters in the model and L is the likelihood value of the model.

[0122] The first round of model refinement: Calculate the AIC value AIC9 of the full model with 9 parameters, remove 1 parameter respectively, and recalculate the parameter value. The algorithm is: bias vector F 花 and the iteration matrix f 花 Remove the row and column elements at the corresponding positions, and keep the other conditions the same. Calculate the AIC value and select the model with the smallest AIC value that is smaller than AIC9 as AIC8.

[0123] Second round of model refinement: The AIC8 model with 8 parameters was selected, and the same pattern as the previous round was used. One parameter was removed respectively, and the parameter values ​​were recalculated. The AIC value was calculated, and the model with the smallest AIC value that was smaller than the AIC9 value was selected.

[0124] After multiple rounds of parameter reduction, the AIC value is calculated until the AIC value is no longer small.

[0125] The number of microscopic examination slides included in the final statistical analysis must be no less than 250, and the calculation program must be written in R language.

[0126] The R language program for data processing of seed setting rate and pollen microscopy is as follows:

[0127] 1. Fruit setting rate

[0128] ss=c();tp=c();td=c()# Input single ear fruiting rate and corresponding daily average temperature and daily minimum temperature

[0129] B<-c(-1,-0.04,-0.05)

[0130] rslt<-Newtons(funs,ss,tp,td,B)

[0131] Tqd<-(-3.892-rslt$root[1]) / (rslt$root[2]+rslt$root[3])

[0132] rslt$root;Tqd

[0133] Newtons<-function(funs,ss,tp,td,B,ep=1e-5,it_max=100){

[0134] index<-0; k<-1

[0135] while(k<=it_max){

[0136] B1<-B; obj<-funs(ss,tp,td,B)

[0137] B<-B-solve(obj$J,obj$F);

[0138] norm<-sqrt((B-B1)%*%(B-B1))

[0139] if(norm <ep){

[0140] index<-1; break

[0141] }

[0142] k<-k+1

[0143] }

[0144] obj<-fun(ss,tp,td,B);

[0145] list(root = B, it = k, index = index, FunVal = obj$F)

[0146] }

[0147] funs <- function(ss, tp, td, B) {

[0148] SS <- c(sum(ss), sum(ss * tp), sum(ss * td))

[0149] N <- length(ss); c1 <- rep(1, N)

[0150] dat <- cbind(c1, tp, td); dat <- as.matrix(dat)

[0151] B <- as.matrix(B); C <- dat %*% B

[0152] sp <- exp(C) / (1 + exp(C))

[0153] SP <- c(sum(sp), sum(sp * tp), sum(sp * td))

[0154] F <- SS - SP

[0155] J <- matrix(c(sum(sp * (sp - 1)), sum(sp * (sp - 1) * tp), sum(sp * (sp - 1) * td), sum(sp * (sp - 1) * tp), sum(sp * (sp - 1) * tp^2), sum(sp * (sp - 1) * tp * td), sum(sp * (sp - 1) * td), sum(sp * (sp - 1) * tp * td), sum(sp * (sp - 1) * td^2)), nrow = 3, byrow = T)

[0156] list(F = F, J = J)

[0157] }

[0158] 2. Pollen microscopy

[0159] h1 <- c(); h2 <- c(); h3 <- c(); tp <- c(); td <- c()

[0160] B <- c(-0.3, -0.012, -0.015, -0.3, -0.012, -0.015, -0.3, -0.012, -0.015)

[0161] m<-rep(0,9)

[0162] AC<-AAIC1(Newton,tp,td,h1,h2,h3,B,m)

[0163] AIC<-rep(0,9)

[0164] AIC[1]<-AC$AAIC;AICMN<-AIC[1]

[0165] for(iin 2:9){

[0166] B<-c(-0.3,-0.012,-0.015,-0.3,-0.012,-0.015,-0.3,-0.012,-0.015)

[0167] AICC<-rep(0,9);mm<-m

[0168] for(j in 1:9){

[0169] m<-mm

[0170] m[j]<-1;B[which(m==1)]=0

[0171] oaic<-AAIC1(tp,td,h1,h2,h3,B,m)

[0172] AICC[j]<-oaic$AAIC

[0173] }

[0174] m<-mm

[0175] m[which(min(AICC))]<-1

[0176] if(min(AICC)<AICMN){

[0177] AIC[i]<-min(AICC)

[0178] AICMN<-min(AICC)

[0179] }

[0180] else break

[0181] }

[0182] oaic1<-AAIC1(tp,td,h1,h2,h3,B,m)

[0183] B<-oaic1$B

[0184] AAIC;AICMN;m;B

[0185] AAIC1<-function(Newton,tp,td,h1,h2,h3,B,m){

[0186] Ob<-Newton(tp,td,h1,h2,h3,B,m)

[0187] B<-Ob$B;N<-length(h1);cl<-rep(1,N);dat<-cbind(cl,tp,td)

[0188] B1<-data.frame(B[1],B[2],B[3]);B1<-as.matrix(B1);C1<-dat%*%B1

[0189] B2<-data.frame(B[4],B[5],B[6]);B2<-as.matrix(B2);C2<-dat%*%B2

[0190] B3<-data.frame(B[7],B[8],B[9]);B3<-as.matrix(B3);C3<-dat%*%B3

[0191] l1<-sum(C1*h1)+sum(C2*h2)+sum(C3*h3)

[0192] l2<-sum(log(1+exp(C1)+exp(C2)+exp(C3))

[0193] b<-9-sum(m);l<-l1-l2;AIC<-2*b-2*l

[0194] list(AAIC=AIC,B=B)}

[0195] Newton<-function(funs,h1,h2,h3,tp,td,B,m,ep=1e-5,it_max=100){

[0196] index<-0;k<-1

[0197] while(k<=it_max){

[0198] obj<-funs(h1,h2,h3,tp,td,B,m)

[0199] Bm<-rep(0,(9-sum(m)))

[0200] if(m[9]==1){B[9]<-0}

[0201] for(i in 8:1){

[0202] if(m[i]==1){

[0203] for(j in(i+1):9){

[0204] B[j-1]<-B[j]

[0205] }}}

[0206] for i in 1:(9-sum(m)){

[0207] Bm[i]<-B[i]

[0208] }

[0209] B<-Bm;B1<-B

[0210] B<-B-solve(obj$J,obj$F);

[0211] norm<-sqrt((B-Bl)%*%(B-Bl))

[0212] Bk<-rep(0,9)

[0213] for(i in 1:(9-(sum(m))){

[0214] Bk[i]<-B[i]}

[0215] for i in 1:8{

[0216] ifm[i]==1{

[0217] forj in 9:(i+1){

[0218] Bk[j]<-Bk[j-1]

[0219] }

[0220] Bk[i]<-0

[0221] }}

[0222] B<-Bk

[0223] if(norm<ep){

[0224] index<-1;break

[0225] }

[0226] k<-k+1

[0227] }

[0228] obj<-funs(h1,h2,h3,tp,td,B,m)

[0229] list(B=B,it=k,index=index,F=obj$F)

[0230] }

[0231] funs<-function(h1,h2,h3,tp,td,B,m){

[0232] H<-c(sum(h1),sum(h1*tp),sum(h1*td),sum(h2),sum(h2*tp),sum(h2*td),

[0233] sum(h3),sum(h3*tp),sum(h3*td))

[0234] N<-length(h1);cl<-rep(1,N);dat<-cbind(cl,tp,td)

[0235] B1<-data.frame(B[1],B[2],B[3]);B1<-as.matrix(B1);C1<-dat%*%B1

[0236] B2<-data.frame(B[4],B[5],B[6]);B2<-as.matrix(B2);C2<-dat%*%B2

[0237] B3<-data.frame(B[7],B[8],B[9]);B3<-as.matrix(B3);C3<-dat%*%B3

[0238] p1<-exp(C1) / (1+exp(C1)+exp(C2)+exp(C3))

[0239] p2<-exp(C2) / (1+exp(C1)+exp(C2)+exp(C3))

[0240] p3<-exp(C3) / (1+exp(C1)+exp(C2)+exp(C3))

[0241] P<-c(sum(p1),sum(p1*tp),sum(p1*td),sum(p2),sum(p2*tp),sum(p2*td),sum(p3)

[0242] ,sum(p3*tp),sum(p3*td))

[0243] FF<-H-P

[0244] JJ<-matrix(

[0245] c(sum(p1*(p1-1)),sum(p1*(p1-1)*tp),sum(p1*(p1-1)*td),sum(p1*p2),sum(p1*p2*tp),sum(p1*p2*td),sum(p1*p3),sum(p1*p3*tp),sum(p1*p3*td),

[0246] sum(p1*(p1-1)*tp),sum(p1*(p1-1)*tp^2),sum(p1*(p1-1)*tp*td),sum(p1*p2*tp),sum(p1*p2*tp^2),sum(p1*p2*tp*td),sum(p1*p3*tp),sum(p1*p3*tp^2),sum(p1*p3*td),

[0247] sum(p1*(p1-1)*td),sum(p1*(p1-1)*tp*td),sum(p1*(p1-1)*td^2),sum(p1*p2*td),sum(p1*p2*tp*td),sum(p1*p2*td^2),sum(p1*p3*td),sum(p1*p3*tp*td),sum(p1*p3*td^2),

[0248] sum(p1*p2),sum(p1*p2*tp),sum(p1*p2*td),sum(p2*(p2-1)),sum(p2*(p2-1)*tp),sum(p2*(p2-1)*td),sum(p2*p3),sum(p2*p3*tp),sum(p2*p3*td),

[0249] sum(p1*p2*tp),sum(p1*p2*tp^2),sum(p1*p2*tp*td),sum(p2*(p2-1)*tp),sum(p2*(p2-1)*tp^2),sum(p2*(p2-1)*tp*td),sum(p2*p3*tp),sum(p2*p3*tp^2),sum(p2*p3*tp*td),

[0250] sum(p1*p2*td),sum(p1*p2*tp*td),sum(p1*p2*td^2),sum(p2*(p2-1)*td),sum(p2*(p2-1)*tp*td),sum(p2*(p2-1)*td^2),sum(p2*p3*td),sum(p2*p3*tp*td),sum(p2*p3*td^2),

[0251] sum(p1*p3),sum(p1*p3*tp),sum(p1*p3*td),sum(p2*p3),sum(p2*p3*tp),sum(p2*p3*td),sum(p3*(p3-1)),sum(p3*(p3-1)*tp),sum(p3*(p3-1)*td),

[0252] sum(p1*p3*tp),sum(p1*p3*tp^2),sum(p1*p3*tp*td),sum(p2*p3*tp),sum(p2*p3*tp^2),sum(p2*p3*tp*td),sum(p3*(p3-1)*tp),sum(p3*(p3-1)*tp^2),sum(p3*(p3-1)*tp*td),

[0253] sum(p1*p3*td),sum(p1*p3*tp*td),sum(p1*p3*td^2),sum(p2*p3*td),sum(p2*p3*tp*td),sum(p2*p3*td^2),sum(p3*(p3-1)*td),sum(p3*(p3-1)*tp*td,sum(p3*(p3-1)*td^2)),

[0254] nrow=9,byrow=T)

[0255] F<-rep(0,(9-sum(m)))

[0256] J<-matrix(rep(0,(9-sum(m))*(9-sum(m))),nrow=(9-sum(m)),byrow=T)

[0257] if(m[9]==1){

[0258] FF[9]=0

[0259] for i in 1:9{

[0260] JJ[9,i]<-0

[0261] JJ[i,9]<-0

[0262] }

[0263] }

[0264] for(iin 8:1){

[0265] if(m[i]==1){

[0266] for(j in(i+1):9){

[0267] FF[j-1]<-FF[j]

[0268] for(k in 1:9){

[0269] JJ[(j-1),k]<-JJ[j,k]

[0270] }

[0271] for k in 1:9{

[0272] JJ[k,(j-1)]<-JJ[k,j]

[0273] }

[0274] }

[0275] For iin 1:(9-sum(m)){

[0276] F[i]<-FF[i]

[0277] forj in 1:(9-sum(m)){

[0278] J[i,j]<-JJ[i,j]}

[0279] }}

[0280] list(F=F,J=J)

[0281] }

[0282] The above contents are merely examples and explanations of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in a similar manner. As long as they do not deviate from the structure of the present invention or exceed the scope defined by the claims, they shall all fall within the protection scope of the present invention.

Claims

1. A method for identifying the fertility transformation characteristics of a photothermosensitive two-line sterile rice line at high altitude, characterized in that: The following steps are involved: (1) Select high-altitude fields to grow rice; (2) Sterile lines are sown in stages and seedlings are transplanted; (3) Determine the field temperature of the planting plot; (4) After heading, the rice is regularly bagged and selfed and the pollen is examined under a microscopic microscope; (5) The data obtained from bagging self-pollination and pollen microscopy were processed using a logistic regression model.

2. The method for identifying fertility conversion characteristics of photothermosensitive two-line sterile rice at high altitude according to claim 1, characterized in that: In the step (1), conventional methods are adopted for seed soaking, germination and seedling raising, the seedling age is 25-30 days, and the sterile seedlings are transplanted to the high altitude field, and the field management is carried out according to conventional methods.

3. The method for identifying fertility conversion characteristics of photothermosensitive two-line sterile rice at high altitude according to claim 1, characterized in that: In the step (1), the high altitude field is located in the middle and lower reaches of the Yangtze River at 29.5-30.5° north latitude, with an altitude of 700-750 meters. A plurality of automatic temperature recorders are installed in the sterile line transplanting field and are set to measure the temperature at the same time.

4. The method for identifying fertility conversion characteristics of photothermosensitive two-line sterile rice at high altitude according to claim 1, characterized in that: In the step (4), the sterile lines are bagged when they begin to head, and ears with stems that are 2 cm from the head but have not yet flowered are selected for bagging and self-pollination, and the percentage of fruiting spikelets to total spikelets is used as the bagging fruit setting rate.

5. The method for identifying fertility conversion characteristics of photothermosensitive two-line sterile rice at high altitude according to claim 1, characterized in that: In the step (4), samples are taken regularly from the beginning of heading to the completion of heading of the identified sterile line, and the stem ears that have not bloomed are selected for microscopic examination. The anthers of 5-6 spikelets are randomly taken from each sampled ear to make a pollen microscopic observation slide, and the pollen is stained with 2% KI-I2 solution, pressed into a slide, and observed under an optical microscope.

6. The method for identifying fertility conversion characteristics of photothermosensitive two-line sterile rice at high altitude according to claim 1, characterized in that: In the step (5), the mathematical model of bagging self-crossing is as follows: p 实i =exp(β 实0 +b 实平 *t 平i +b 实低 *t 低i ) / (1+exp(β 实0 +b 实平 *t 平i +b 实低 *t 低i )) p 不i =1 / (1+exp(β 实0 +b 实平 *t 平i +b 实低 *t 低i )) p 实i +p 不i =1,m 实i +m 不i =1; In the formula, p 实i and p 不i They represent the theoretical probability of the i-th self-crossing bag to produce fruit or not, β 实0 , β 实平 and β 实低 are the parameters of the model, representing the intercept of the fruiting rate in the logistic regression model, the slope of the daily average temperature, and the slope of the daily minimum temperature, t 平i and t 低i are the average daily temperature and the average daily minimum temperature of the sampling plot on the 13th to 15th day from the bagging date of the i-th self-pollination bag, m 实i and m 不i They represent the actual fruit setting rate and non-fruit setting rate of rice ears in the i-th self-pollination bag respectively; The self-fertilization rate of 2% is taken as the critical point of fertility transformation of the sterile line. According to the definition of the starting point temperature of the sterile line, the starting point temperature T = t 平 =t 低 , where t 平 and t 低 They represent the daily average temperature and daily minimum temperature of the sterile line during its sensitive period. The calculation formula for the fertility threshold temperature of the sterile line is: T = (-3.892-β 实0 ) / (β 实平 +β 实低 ).

7. The method for identifying fertility conversion characteristics of photothermosensitive two-line sterile rice at high altitude according to claim 6, characterized in that: In step (5), the calculation method of bagging firmness is as follows: Use the maximum likelihood method to solve: The likelihood value L 实 Take the natural logarithm l 实 : The maximum likelihood theory holds that the likelihood value L 实 The parameter value in the largest case is the unbiased estimate of the model, which is also l 实 It is also the largest; Ask for l 实 Maximum, l 实 β 实0 , β 实平 and β 实低 The partial derivative of DP is 0; 实0 , DP 实平 and DP 实低 Respectively expressed as l 实 β 实0 , β 实平 and β 实低 Partial guide; Let parameter vector B = (β0, β 实平 ,β 实低 ) T and deflection vector F = (PD 实0 ,PD 实平 ,PD 实低 ) T , F is the function vector of B, which is solved by Newton iteration method. The Jacobi matrix f used for iteration is the partial derivative matrix function of F with respect to B; The initial value is set artificially, and the iterative formula is: B (m+1) =B (m) -f (-1) (B (m) )*F(B (m) ), m is the number of iterations, iterate to ||B (m+1) -B (m) ||<10 -5 In case B (m+1) The value is the B parameter vector value, B (m) and B (m+1) Respectively represent the B vector values ​​after the mth and m+1th iterations, f (-1) (B (m) ) represents the inverse matrix of the m-th iteration of the f matrix, F(B (m) ) represents the F vector of iteration m.

8. The method for identifying fertility conversion characteristics of photothermosensitive two-line sterile rice at high altitude according to claim 1, characterized in that: In step (5), the mathematical model of pollen microscopy is as follows: p 典i =exp(β 典0 +b 典平 *t 平i +b 典低 *t 低i ) / (1+exp(β 典0 +b 典平 *t 平i +b 典低 *t 低i )+exp(β 园0 +b 园平 *t 平i +b 园低 *t 低i )+exp(β 染0 +b 染平 *t 平i +b 染低 *t 低i )) p 园i =exp(β 园0 +b 园平 *t 平i +b 园低 *t 低i ) / (1+exp(β 典0 +b 典平 *t 平i +b 典低 *t 低i )+exp(β 园0 +b 园平 *t 平i +b 园低 *t 低i )+exp(β 染0 +b 染平 *t 平i +b 染低 *t 低i )) p 染i =exp(β 染0 +b 染平 *t 平i +b 染低 *t 低i ) / (1+exp(β 典0 +b 典平 *t 平i +b 典低 *t 低 i)+exp(β 园0 +b 园平 *t 平i +b 园低 *t 低i )+exp(β 染0 +b 染平 *t 平i +b 染低 *t 低i )) p 可i =1 / (1+exp(β 典0 +b 典平 *t 平i +b 典低 *t 低i )+exp(β 园0 +b 园平 *t 平i +b 园低 *t 低i )+exp(β 染0 +b 染平 *t 平i +b 染低 *t 低i )) pp 典i + p 园i + p 染i + p 可i =1m 典i +m 园i +m 染i +m 可i =1 In the formula, p 典i 、p 园i 、p 染i 、p 可i represent the theoretical probabilities of typical failed pollen, round failed pollen, stained failed pollen and stainable pollen in the i-th microscopic examination respectively; as the parameter value of the model, β 典0 , β 典平 and β 典低 are the intercept of pollen failure, the slope of daily average temperature and the slope of daily minimum temperature, respectively. 园0 , β 园平 and β 园低 are the intercept of pollen abortion, the slope of daily average temperature and the slope of daily minimum temperature, β 染0 , β 染平 and β 染低 are the intercept of pollen atrophy, the slope to the daily average temperature, and the slope to the daily minimum temperature, respectively; t 平i and t 低i The average of the daily average temperature and the daily minimum temperature of the sampling plot on the 13th to 15th day before the i-th bagging date, m 典i 、m 园i 、m 染i and m 可i They represent the ratios of typical failed, round failed, stained failed and stainable pollen in the i-th microscopic observation respectively.

9. The method for identifying fertility conversion characteristics of photothermosensitive two-line sterile rice at high altitude according to claim 8, characterized in that: In step (5), the calculation method of pollen microscopy is as follows: A similar maximum likelihood method is used to solve: The likelihood value L 花 Take the natural logarithm l 花 : According to the maximum likelihood theory, the likelihood value L 实 The parameter value under the maximum condition is the unbiased estimate of the model. 实 Maximum; let B 花 =(β 典0 ,β 典低 ,β 园0 ,β 园平 ,β 园低 ,β 染0 ,β 染平 ,β 染低 ) T As the parameter vector of the model, according to the theory of calculus, l 实 To B 花 The deflection vector F 花 When l is 0, 实 maximum; F 花 =(PD 典0 ,PD 典平 ,PD 典低 ,PD 园0 ,PD 园平 ,PD 园低 ,PD 染0 ,PD 染平 ,PD 染低 ) T ; Let vector F 花 That is, 9 partial derivatives are 0, 9 equations are constructed, and 9 parameter values ​​are solved. The 9 equations are nonlinear, and highly approximate solutions are obtained through Newton iteration. The Jacobi matrix f used in Newton iteration is 花 Yes F 花 To B 花 The partial derivative matrix function of ; The initial value is set artificially, and the iteration formula is: m refers to the number of iterations. The situation Value is B 花 parameter vector value; and Respectively represent B after the mth and m+1th iterations 花 vector value, Indicates the mth iteration of f 花 The inverse matrix of the moment, represents the F of the mth iteration 花 vector.

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